Those are of the form "set A= set B" or (statement 1-2 (a)) "statement A implies statement B" .
To prove "set A= set B" first show that any member of A is necessarily a member of B (so that A is a subset of B), then turn around and show that any member of B is a member of A (so that B is a subset of A).
For example, the first one says the complement of (M union N) is equal to (complement of M) intersect (complement of N).
I presume you know that the "complement" of a set, A, is the set of elements, in the "universal set" that are NOT in A, that the "union" of two sets is the set of all elements that are in either set, and that the "intersection" of two sets is the set of all elements that are in both. For example if the universal set is {a, b, c, d, e, f, g} then the complement of {a, d, f} is {b, c, e, g}, the union of {a, d, f} and {a, c, f, g} is {a, c, d, f, g}, and the intersection of {a, d, f} and {a, c, f, g} is {a, f}.
To show that the complement of (M union N) is equal to (complement of M) intersect (complement of N), start
Suppose x is in complement of (M union N). Then x is not in M union N which means x is in neither M nor N. So x is in complement of M and in complement of N which means it is in (complement of M) intersect (complement of N).
That proves that (M union N) is a SUBSET of (complement of M) intersect (complement of N). Now we need to prove "the other way around" which we do in basically the same way.
Suppose y is in (complement of M) intersect (complement of N). Then y must be in both (complement of M) and (complement of N). Since y is in the complement of M it is not in M. Since y in the complement of N, it is not in N. y is not in M union N so it is in the complement of M union N.
